Consider the following reactions at 300 K.
A `rarr` B (uncatalysed reaction)
`Aoverset("catalyst")rarrB` (catalyst reaction)
The activation energy is lowered by `8.314"KJ mol"^(-1)` for the catalysed reaction. How many times the rate of this catalysed reaction greater than that of uncatalysed reaction?(Given `e^(3.33)=20)`

Options

A. 28 times
B. 15 times
C. 25 times
D. 22 times that of uncatalysed reaction.

Answer

A

Explanation

`K_("uncat") = Ae^(-E_("uncat")//RT)`
`K_("cat") =Ae^(-E_("cat")//RT)`
Let the `E_(a)` for uncatalysed reaction be A, then for catalysed reaction it will be `(A-8.314 xx 10^(3))` calories/mol.
`K_("cat")/K_("uncat") =(e^(-A-8.314 xx 10^(3))//RT)/(e^(-A//RT)) = e^(8.314 xx 10^(3)//RT) = e^(33) = 28`